Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13304 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C61 · Schur multiplier (H2) = C22 |
| direct product | C61×#13538 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C61 | C2×D8 |
| commutator, Frattini, cosocle | C22×C8 | C23×C61 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C61 ◁ C2×C42×C61 ◁ C2×C4×C8×C61 ◁ G | |
294 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 15616 |
A minimal faithful permutation representation — 3 generators on 93 points:
(1,2,5,7)(3,8,4,6)(9,10)(11,13)(12,14)(15,16)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93);(1,3,5,4)(2,6,7,8)(9,11,12,15)(10,13,14,16)(17,18,21,25)(19,22,28,31)(20,29,27,24)(23,32,30,26);(1,4,5,3)(2,6,7,8)(10,14)(13,16)(18,22)(19,26)(20,27)(23,24)(25,31)(28,32)(29,30)3172 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 6526);